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6.2
Tests of Significance
Example #1
borrowers at private 4year college:
mean debt (
a
)= $21,200 (survey result)
borrowers at public 4year college:
mean debt (
b
)= $17,100 (survey result)
the difference $4100 (
a

b
) is fairly large/ but these numbers are estimates
of the true means
Can we conclude from these data that the private 4year students have greater debt than public
fouryear borrowers (that the two populations means are different)?
Could ask:
What is the probability of obtaining a difference as large or larger than the observed
$4100 assuming, in fact, there is no difference in the true means?
probability big→ our result is not rare when the population means are the same→ do not
conclude that the population means are different
probability small→ our result is rare when the population means are the same→ do conclude that
the population means are different
computed prob is 0.17 (do later in book)/ this prob is not particularly small (0.05 standard)
Conclude:
The data do not provide evidence for us to conclude that the mean debts for private
fouryear and public fouryear borrowers are different.
There is no evidence to question the
possibility that the true difference is zero.
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View Full Document Example #2
1997 mean debt for undergraduate study (
c
) was $11,400 (survey result)
2002 mean debt for undergraduate study (
d
) was $18,900 (survey result)
the difference $7500 is fairly large (
d

c
)/ but these numbers are estimates
of the true means
Can we conclude from these data that there is an increase in borrowing over this period (that the
two population means are different)?
Could ask:
What is the probability of obtaining a difference as large or larger than the observed
$7500 assuming, in fact, there is no difference in the true means?
computed probability is 0.00004 (do later in book)/ this probability is very small (0.05 standard)
probability big→ our result is not rare when the population means are the same→ do not
conclude that the population means are different
probability small→ our result is rare when the population means are the same→ do conclude that
the population means are different
Conclude:
The data do provide evidence for us to conclude that there is increased borrowing
over this period.
The evidence suggests that the assumption that underlies the calculation (no
difference in mean debt) is not true.
2
Stating hypotheses
Null hypothesis
H
0
The statement being tested in a test of significance is called the null hypothesis
.
The test of
significance is designed to assess the strength of the evidence against the null hypothesis.
Usually the null hypothesis is a statement of “no effect” or “no difference.”
EX 1
 H
0
:
there is no difference in the true means
we try to find evidence
against
the null hypothesis
Alternative hypothesis
H
a
The alternative hypothesis
is the statement we hope or suspect is true instead of H
0
.
EX 1
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This note was uploaded on 02/23/2011 for the course STAT 2700 taught by Professor Bill during the Spring '11 term at Adelphi.
 Spring '11
 Bill

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